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The purpose of this paper is to propose a new method for computing validities in the multimodel approach.

The multimodel approach offers an interesting alternative and a powerful tool to bypass the difficulties to model, control and diagnose a nonlinear and complex system. Its idea is defined as the apprehension of a nonlinear behaviour of a system by a set of local models characterizing the system operation in different operating zones. In spite of the success of its application in different fields, many problems related to the synthesis of multimodel approach remain open. These include, in particular, the method of obtaining the contribution degrees, also called validities, of the base-models for the deduction of the multimodel output.

The presented method may lead to superior results in comparison with the residue approach commonly used in the calculation of validities. Numerical simulation results and an experimental validation on a semi-batch reactor clearly illustrated the effectiveness of the proposed method and proved its impact on the improvement of the performances of the multimodel approach. Moreover, the multimodel approach using the new validities’ computation method can lead to perfect modelling of the process.

The proposed method discussed in the paper has the potential to make the multimodel approach more efficient in the modelling of complex real systems.

A significant contribution of the paper is the formulation of a new constrained optimization problem that can be solved by using a powerful mathematical tool such as the active set method, allowing to estimate the validity indexes in the multimodel approach. The obtained optimal solution can lead to perfect modelling of nonlinear and complex real systems.